Question

How do you find the derivative of `f(x)=3` using the limit process?

Answer 1

The limit definition of the derivative takes a function `f` and states its derivative equals `f'(x)=lim_(hrarr0)(f(x+h)-f(x))/h`.

So, when `f(x)=3`, we see that `f(x+h)=3` as well, since `3` is a constant with no variable.

Thus, `f'(x)=lim_(hrarr0)(3-3)/h=lim_(hrarr0)0/h=lim_(hrarr0)0=0`.